39 persons can repair a road in 12 days, working 5 hours per day. In how many days will 30 persons, working 6 hours per day, complete the work?

Concept / Approach

• Work is proportional to (persons) × (hours per day) × (days) when efficiency is constant.

Step-by-step calculationTotal work (person-hours) = 39 × 5 × 12 = 2340Daily capacity with 30 persons at 6 h/day = 30 × 6 = 180 person-hours/dayDays required = 2340 ÷ 180 = 13

Verification13 × 180 = 2340 person-hours, equal to the original work.

Final Answer13 days